Articles de revistahttp://hdl.handle.net/2117/3339
Tue, 26 Sep 2017 19:58:07 GMT2017-09-26T19:58:07ZOn the phase-lag with equation with spatial dependent lagshttp://hdl.handle.net/2117/106377
On the phase-lag with equation with spatial dependent lags
Liu, Zhuangyi; Quintanilla de Latorre, Ramón; Wang, Yang
In this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.
Thu, 13 Jul 2017 11:42:19 GMThttp://hdl.handle.net/2117/1063772017-07-13T11:42:19ZLiu, ZhuangyiQuintanilla de Latorre, RamónWang, YangIn this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.On uniqueness and stability for a thermoelastic theoryhttp://hdl.handle.net/2117/105157
On uniqueness and stability for a thermoelastic theory
Quintanilla de Latorre, Ramón
In this paper we investigate a thermoelastic theory obtained from the Taylor approximation for the heat flux vector proposed by Choudhuri. This new thermoelastic theory gives rise to interesting mathematical questions. We here prove a uniqueness theorem and instability of solutions under the relaxed assumption that the elasticity tensor can be negative. Later we consider the one-dimensional and homogeneous case and we prove the existence of solutions. We finish the paper by proving the slow decay of the solutions. That means that the solutions do not decay in a uniform exponential way. This last result is relevant if it is compared with other thermoelastic theories where the decay of solutions for the one-dimensional case is of exponential way.
Tue, 06 Jun 2017 09:59:07 GMThttp://hdl.handle.net/2117/1051572017-06-06T09:59:07ZQuintanilla de Latorre, RamónIn this paper we investigate a thermoelastic theory obtained from the Taylor approximation for the heat flux vector proposed by Choudhuri. This new thermoelastic theory gives rise to interesting mathematical questions. We here prove a uniqueness theorem and instability of solutions under the relaxed assumption that the elasticity tensor can be negative. Later we consider the one-dimensional and homogeneous case and we prove the existence of solutions. We finish the paper by proving the slow decay of the solutions. That means that the solutions do not decay in a uniform exponential way. This last result is relevant if it is compared with other thermoelastic theories where the decay of solutions for the one-dimensional case is of exponential way.On a Caginalp phase-field system with two temperatures and memoryhttp://hdl.handle.net/2117/104992
On a Caginalp phase-field system with two temperatures and memory
Conti, Monica; Gatti, Stefania; Miranville, Alain; Quintanilla de Latorre, Ramón
The Caginalp phase-field system has been proposed in [4] as a simple mathematical model for phase transition phenomena. In this paper, we are concerned with a generalization of this system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory, apt to describe transition phenomena in nonsimple materials. The model consists of a parabolic equation governing the order parameter which is linearly coupled with a nonclassical integrodifferential equation ruling the evolution of the thermodynamic temperature of the material. Our aim is to construct a robust family of exponential attractors for the associated semigroup, showing the stability of the system with respect to the collapse of the memory kernel. We also study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.
The final publication is available at Springer via https://doi.org/10.1007/s00032-017-0263-z
Mon, 29 May 2017 11:37:49 GMThttp://hdl.handle.net/2117/1049922017-05-29T11:37:49ZConti, MonicaGatti, StefaniaMiranville, AlainQuintanilla de Latorre, RamónThe Caginalp phase-field system has been proposed in [4] as a simple mathematical model for phase transition phenomena. In this paper, we are concerned with a generalization of this system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory, apt to describe transition phenomena in nonsimple materials. The model consists of a parabolic equation governing the order parameter which is linearly coupled with a nonclassical integrodifferential equation ruling the evolution of the thermodynamic temperature of the material. Our aim is to construct a robust family of exponential attractors for the associated semigroup, showing the stability of the system with respect to the collapse of the memory kernel. We also study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.A well-posed problem for the three-dual-phase-lag heat conductionhttp://hdl.handle.net/2117/104492
A well-posed problem for the three-dual-phase-lag heat conduction
Quintanilla de Latorre, Ramón
Tue, 16 May 2017 10:32:21 GMThttp://hdl.handle.net/2117/1044922017-05-16T10:32:21ZQuintanilla de Latorre, RamónOn (non-)exponential decay in generalized thermoelasticity with two temperatureshttp://hdl.handle.net/2117/103572
On (non-)exponential decay in generalized thermoelasticity with two temperatures
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón; Racke, Reinhard
We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the non-exponential stability for the Lord-Shulman model.
Thu, 20 Apr 2017 10:27:50 GMThttp://hdl.handle.net/2117/1035722017-04-20T10:27:50ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónRacke, ReinhardWe study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the non-exponential stability for the Lord-Shulman model.Thermal stresses in chiral plateshttp://hdl.handle.net/2117/100958
Thermal stresses in chiral plates
Iesan, Dorin; Quintanilla de Latorre, Ramón
This article is concerned with the linear theory of chiral Cosserat thermoelas- tic bodies. We investigate the deformation of chiral plates. First, we present the basic equations which govern the deformation of thin plates. Then, we present reciprocity and uniqueness results. In the next section, we establish the instability of solutions whenever the internal energy is negative. We use a semigroup approach to prove the existence of a solution. The deformation of an in nite plate with a circular hole is investigated.
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Africa Review on 17/04/2014, available online:http://www.tandfonline.com/doi/full/10.1080/01495739.2016.1217180
Tue, 14 Feb 2017 11:05:52 GMThttp://hdl.handle.net/2117/1009582017-02-14T11:05:52ZIesan, DorinQuintanilla de Latorre, RamónThis article is concerned with the linear theory of chiral Cosserat thermoelas- tic bodies. We investigate the deformation of chiral plates. First, we present the basic equations which govern the deformation of thin plates. Then, we present reciprocity and uniqueness results. In the next section, we establish the instability of solutions whenever the internal energy is negative. We use a semigroup approach to prove the existence of a solution. The deformation of an in nite plate with a circular hole is investigated.On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo lawhttp://hdl.handle.net/2117/90781
On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law
Miranville, Alain; Quintanilla de Latorre, Ramón
Our aim in this paper is to study generalizations of the nonconserved and conserved Caginalp phase-¿eld systems based on the Maxwell–Cattaneo law with two temperatures for heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators.
This is the peer reviewed version of the following article: Miranville, A., and Quintanilla, R. (2016) On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law. Math. Meth. Appl. Sci., 39: 4385–4397, which has been published in final form at http://dx.doi.org/10.1002/mma.3867. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Fri, 14 Oct 2016 10:40:07 GMThttp://hdl.handle.net/2117/907812016-10-14T10:40:07ZMiranville, AlainQuintanilla de Latorre, RamónOur aim in this paper is to study generalizations of the nonconserved and conserved Caginalp phase-¿eld systems based on the Maxwell–Cattaneo law with two temperatures for heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators.On the time decay of solutions for non-simple elasticity with voidshttp://hdl.handle.net/2117/89329
On the time decay of solutions for non-simple elasticity with voids
Liu, Zhuangyi; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.
Thu, 28 Jul 2016 11:25:42 GMThttp://hdl.handle.net/2117/893292016-07-28T11:25:42ZLiu, ZhuangyiMagaña Nieto, AntonioQuintanilla de Latorre, RamónIn this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.A Caginalp phase-field system based on type III heat conduction with two temperatureshttp://hdl.handle.net/2117/87512
A Caginalp phase-field system based on type III heat conduction with two temperatures
Miranville, Alain; Quintanilla de Latorre, Ramón
Our aim in this paper is to study a generalization of the Caginalp phasefield
system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We consider here both regular and singular nonlinear terms. Furthermore, we endow the equations with two types of boundary
conditions, namely, Dirichlet and Neumann. Finally, we study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.
Tue, 31 May 2016 07:44:34 GMThttp://hdl.handle.net/2117/875122016-05-31T07:44:34ZMiranville, AlainQuintanilla de Latorre, RamónOur aim in this paper is to study a generalization of the Caginalp phasefield
system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We consider here both regular and singular nonlinear terms. Furthermore, we endow the equations with two types of boundary
conditions, namely, Dirichlet and Neumann. Finally, we study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.On chiral effects in strain gradient elasticityhttp://hdl.handle.net/2117/84128
On chiral effects in strain gradient elasticity
Iesan, Dorin; Quintanilla de Latorre, Ramón
This paper is concerned with the problem of uniformly loaded bars in strain gradient elasticity. We study the deformation of an isotropic chiral bar subjected to body forces, to tractions on the lateral surface and to resultant forces and moments on the ends. Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The three-dimensional problem is reduced to the study of some generalized plane strain problems. The method is used to study the deformation of a uniformly loaded circular cylinder. New chiral effects are presented. The flexure of a chiral cylinder, in contrast with the case of achiral materials, is accompanied by extension and bending. The salient feature of the solution is that a uniform pressure acting on the lateral surface of a chiral circular elastic cylinder produces a twist around its axis.
Thu, 10 Mar 2016 11:28:00 GMThttp://hdl.handle.net/2117/841282016-03-10T11:28:00ZIesan, DorinQuintanilla de Latorre, RamónThis paper is concerned with the problem of uniformly loaded bars in strain gradient elasticity. We study the deformation of an isotropic chiral bar subjected to body forces, to tractions on the lateral surface and to resultant forces and moments on the ends. Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The three-dimensional problem is reduced to the study of some generalized plane strain problems. The method is used to study the deformation of a uniformly loaded circular cylinder. New chiral effects are presented. The flexure of a chiral cylinder, in contrast with the case of achiral materials, is accompanied by extension and bending. The salient feature of the solution is that a uniform pressure acting on the lateral surface of a chiral circular elastic cylinder produces a twist around its axis.